The length of twilight in the tropics is legendarily brief, while at high latitudes it can last for hours. Since parallel rays of sunlight are falling on Earth, shouldn’t twilight be the same everywhere on the globe?

Before we look at this, we first have to nail down what we mean by the term twilight. To a watchstander on a clear, dark night, the first lightening of the eastern sky is clear evidence that the crepuscular interlude has begun. On a moonlit night, however, the first hints of dawn may not be evident until some time later. The effect of artificial light on the eye also diminishes the ability to detect the early signs of twilight.

To eliminate vagaries of weather and human observers, a set of strict astronomical definitions have been derived to define the progression from light to dark. There are three periods of twilight. The shortest period is civil twilight which lasts until the sun (the center of the sun, that is) is six degrees below the horizon. Nautical twilight extends until the sun has dropped 12 degrees below the horizon and astronomical twilight continues until the sun is 18 degrees below the horizon. (Fortunately for this discussion, astronomical twilight is of little practical interest to mariners.)

The strict mathematical definition of civil and nautical twilight provides a framework within which to measure the phenomena. As a rough estimate, the period available to shoot stars is the time between nautical and civil twilight. So we’ll use the term twilight to refer to this period of “useful” twilight.

So, at higher latitudes, this twilight period lasts longer, while the shortest twilight is found in the tropics. (For example, between 23 1/2 degrees north and 23 1/2 degrees south twilight lasts less than half an hour.)

The most dramatic lengthening of twilight due to higher latitudes occurs during the solstices. On the summer solstice at 55 degrees north degreesthe approximate latitude of Belfast, Northern Ireland, and Copenhagen, Denmark – twilight starts at civil twilight in the evening and does not end until the coming of civil twilight again in the morning. This provides an eager navigator with more than four hours of star shooting time. At 40 degrees north – the latitude of northern California and Philadelphia – twilight extends 42 minutes. Meanwhile, south of the equator on the same day, twilight lasts nearly one hour at 60 degrees south – about twice the time of twilight in the tropics.

A lengthened twilight is not simply an effect of the solstice. When the sun is on the equator (0 degrees declination), it might seem as if twilight would be the same at all latitudes. This September 23, the date of autumnal equinox, twilight lasts 24 minutes at the equator; 31 minutes at 40 degrees north and south; and a whopping 50 minutes at 60 degrees north and south. Regardless of the position of the sun, twilight is always longer at high latitudes.

How can this be? What polar influences cause this crepuscular peculiarity? To understand the forces, it is helpful to view Earth from space as if orbiting in the space shuttle. Theoretically, the sun sets or rises when the sun’s geographic position (GP) is 90 degrees from the position of an observer. If one were able to plot the GP, then one could scribe a circle with the GP as its center and a radius of 90 degrees. The area inside the circle (on the GP’s side of the scribed line) would be sunlit and mariners in that area would see the sun; mariners on the other side of the line would be experiencing twilight. We know that civil twilight occurs when the sun is within six degrees of the horizon. Therefore, the edge of civil twilight is 96 degrees from the GP. This may also be drawn as a circle on Earth centered on the GP with a radius of 96anddeg;. The boundary of nautical twilight may be drawn with its radius of 102 degrees.

These three concentric circles are so large that when Earth is viewed from afar, they would appear as three parallel lines passing through the tropics. Wherever the sun’s GP is located, these lines are roughly perpendicular to lines of latitude at the tropics. Take the extreme example where the sun has 0 degrees declination and the mariner is on the equator. First, the three circles run north/south where they intersect the equator and therefore are perpendicular to it. By definition they are six degrees apart. Earth spins 15 degrees each hour, so it will take 6 degrees / 15 degrees = .4 hours or 24 minutes for Earth to rotate enough for civil twilight to become nautical twilight for a mariner located on the equator. This is the length of twilight on the equator at the equinox.

If the sun had a different declination, say 10 degrees north, the three circles would no longer be perpendicular to the equator. The distance measured along the equator from one circle to the next is greater than six degrees. The length of twilight will also increase slightly to around 25 minutes at the equator. It is clear that the farther from perpendicular the intersection of the circles and the equator get, the longer the time of twilight.

This phenomenon also explains the lengthened twilight at high latitudes. As the circles near the poles, their direction changes from a relatively north/south orientation to east/west. Effectively, they turn relative to lines of latitude. The crossing angle between the circles and lines of latitude changes from roughly perpendicular to parallel. (Or for purists, the latitude is tangent to the circle around the GP.) It is in these areas that twilight exends to the point where darkness never falls or the sun never rises during entire days.

While it is easy to determine the length of twilight at the equator when the sun also happens to be on the equator, it is more complicated to predict twilight for other locations and for other times of the year. This may be done for any position on Earth using basic trigonometric formulas commonly used for sight reduction. The first step is to determine LHA of sun at civil twilight. With this and a vessel’s longitude, it is easy to find the sun’s GHA which may be turned into time in the Nautical Almanac.Co-altitude is the distance from GP to a vessel’s position and will be 96 degrees for civil twilight and 102 degrees for nautical twilight.

To determine the time of evening civil twilight and nautical twilight for a vessel at 30 degrees N, 33 degrees W on April 14, it is necessary to obtain declination, which is approximately 9 degrees 30′ N and insert the values for declination, co-altitude and latitude. The formula for civil twilight is:Cos LHA is -0.2189, which means LHA is 102.65 degrees, or 102 degrees 39′. Longitude is 33 degrees W. In the western hemisphere, GHA = LHA + longitude = 102 degrees 39′ + 33 degrees = 135 degrees 39′. Looking at the daily page for April 14 in the Nautical Almanac, GHA is 134 degrees 57.7′ at 2100. The difference, roughly 41′, requires about three minutes, according to the Increments and Corrections table in the back of the Nautical Almanac. GHA of 135 degrees 39′ occurs at approximately 2103 GMT. Using the same procedure, but substituting a co-altitude of 102 degrees, the time of nautical twilight is 2132 GMT. While it is certainly possible to determine time of GHA to the second, that precision is unrealistic because values for both latitude and declination are rough here. It is also unnecessary because for practical purposes, the useful beginning and end of twilight are highly dependent on factors beyond a navigator’s control (i.e., bright stars available, clarity of horizon). In this example, twilight lasts about 29 minutes and a prudent navigator will be on deck ahead of time, in any case.

So the reason for varying length of twilight has to do with nothing more mysterious than the geometry of Earth at is receives the light from the sun. Celestial navigators in the tropics will always have less time to grab their twilight sights than their colleagues at higher latitudes.Cameron Bright